It has been observed that, for rural areas, the prediction of the most recent ITU recommended propagation model (Rec

(1)

3080 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005

Examination of Existent Propagation Models Over Large Inhomogeneous Terrain Proﬁles Using Fast Integral

Equation Solution

Celal Alp Tunc, Ayhan Altintas, and Vakur B. Ertürk

Abstract—The accuracyof most widelyused empirical models are inves- tigated using the spectrallyaccelerated forward-backward (FBSA) method as a benchmark solution. First, FBSA results are obtained for propagation over large scale terrain proﬁles and compared with measurements to as- sess the accuracyof FBSA. Then, accuracyof some International Telecom- munication Union (ITU) and Federal Communications Commission (FCC) propagation models are investigated. It has been observed that, for rural areas, the prediction of the most recent ITU recommended propagation model (Rec. 1546) deviates much more than older models do.

Index Terms—Federal Communications Commission (FCC) curves, forward-backward spectral acceleration (FBSA) method, International Telecommunication Union (ITU) recommendations, propagation models, rough surface scattering.

I. INTRODUCTION

Most of the automated propagation prediction tools for coverage analysis over geometrical databases use empirical models [1]–[5] with or without semi-empirical multiple knife-edge diffraction (MD) losses [6]–[10] in order to predict field strengths over terrain profiles. These empirical models which are described byequations or curves derived from statistical analysis of a large number of measured data, are simple and do not require details of the terrain. Therefore, theyare easyand fast to apply. However, they cannot provide a very accurate estimation of the scattered field or the path loss for an arbitraryenvironment.

Hence, comparison of empirical models in terms of accuracyis an important issue for the prediction of ﬁeld strengths over large terrain proﬁles.

In this paper, a detailed investigation of some of the most widelyused empirical propagation models with or without MD corrections has been performed using the spectrallyaccelerated forward-backward (FBSA) method [11]–[13] as a benchmark solution, after its accuracyis compared with measurements. Furthermore, the good agreement between the FBSA and measured results conﬁrm the consistencyof the method to be used for a section of the three-dimensional (3-D) environment, though the FBSA is based on the two-dimensional (2-D) Green’s function. Use of other 2-D Green’s function based integral equations for 3-D environments has been presented in the literature before [14]–[21].

We have chosen the FBSA among these methods, because of itsO(N) computational cost, to examine the propagation models over electricallylarge terrain proﬁles.

Interestingly, it has been observed that, for rural areas, the most recent International Telecommunication Union (ITU) recommended propagation model (Rec.-1546) needs to be modified. Furthermore, the use of MD losses in conjunction with empirical solutions increases the error if the field strength or the path loss due to the empirical model is alreadylower than that of the reference solution. Therefore, results of this studymayhelp in the choice of the most suitable empirical models or in the development of more robust propagation techniques. A robust technique for the prediction of field strengths over large terrain profiles must be polarization and frequencydependent, and must take electrical properties, and details of the terrain profile into account.

Manuscript received November 12, 2004; revised March 10, 2005.

The authors are with the Department of Electrical and Electronics Engineering, Bilkent University, Ankara 06800, Turkey (e-mail:

celal@ee.bilkent.edu.tr).

Digital Object Identiﬁer 10.1109/TAP.2005.854548

Fig. 1. Generic terrain proﬁle.

In Section II, the integral equation (IE) formulation and its solution using the FBSA is brieﬂydiscussed. Numerical results are presented in Section III where the accuracyof existing empirical propagation models are compared. Finally, some concluding remarks are presented.

Ane^jwttime convention is used and suppressed from the expressions.

II. FORMULATION

The scattered field over an electricallylarge rough terrain profile which is illuminated byan incident electromagnetic field {Eînc(), Hînc()} ( = ^xx + ^zz) is computed using an IE based method to be used as a reference solution. Fig. 1 illustrates such a rough surface that is characterized with the curve C defined by z = f(x), along the x-axis. Considering the terrain as an imperfect conductor (r(); r()) and using the Impedance boundaryconditions (IBC) [22], an electric field integral equation (EFIE) for a transverse magnetic (TM_y) polarization can be written in terms of the equivalent electric current densityJyon the surface as

0E_y^inc() = 0s()Jy() 0 j!

CJy(⁰)G(; ⁰)d⁰ +

Cs(⁰)Jy(⁰) @@n⁰G(; ⁰)d⁰ (1) whereas a magnetic ﬁeld integral equation (MFIE) for the transverse electric (TE_y) polarization case can be obtained in terms of the tangen- tial induced currentJtas

0Hy^inc() = Jt() 0

CJt(⁰) @@n⁰G(; ⁰)d⁰

+j! Cs(⁰)Jt(⁰)G(; ⁰)d⁰: (2)

In (1) and (2), s is the surface impedance along the surface, G(; ⁰) = H₀⁽²⁾(; ⁰)=4j is the 2-D Green’s function and (@=@n⁰)G(; ⁰) denotes its derivative with respect to ^n⁰, the normal vector to the surface at the radiating point⁰. It is noted that TM_yand TE_ydeﬁnitions used here are with respect toy-coordinate.

Assuming that the incident field is of finite extent in space, the surface and integrals in (1) and (2) can be confined to a finite region, though the profileC is arbitrarilyextended to infinity. Therefore, (1) and (2) can be solved using a point-matching moment method solution leading to the matrix equation in the form of

V = Z 1 I (3)

where I contains the unknown current coefﬁcients Im, Z is the impedance matrix whose entries are given in [13], andV denotes the incident ﬁeld evaluated at the matching points.

(2)

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 3081

Fig. 2. Path loss over Hadsund terrain proﬁle. (a) Proﬁle geometry. (b) TM polarization at 435 MHz.Distance = 7950 m, 1 = 0 1 , =

115 275, = 117, = 13 .

Instead of the direct solution of the system defined by (3), which requiresO(N³) operations, the FBSA (O(N)) is used in order to find the unknown current coefficients for electricallyverylarge terrains. For further details on the FBSA, the reader is referred to [12] and [13].

III. NUMERICALRESULTS ANDDISCUSSION

A. Validation of the FBSA for Real World Propagation Problems In order to assess the accuracyof the FBSA as well as to demon- strate its consistencywith measurements, comparisons of FBSA results with measurements are shown in Figs. 2 and 3. The terrain profiles are from Denmark with lengths up to 8 km. The height variations are of the order 20–50 m. Measured data were obtained byHviid et al. [14] using a dipole with a transmitted power of 10 W and a gain of 8 dBi. The transmitter height is 10.4 m. The receiver antenna is a=4 monopole on top of a van with a height of 2.4 m. Having no exact information about the vegetation and electrical properties of terrains, the surface impedances are taken ass= 20:2 + j8:1 in order to handle some small forests and other land cover data along the profiles [14]. Also shown in the figures are the computations of Hviid et al. [14] with a different terrain based integral equation method. This method neglects the backscattering, has a computational cost ofO(N²), assumes per- fect magnetic conductor terrain, and it can onlyhandle the TM polarization case. We have taken the segment length=10, and the strong region length,Ls = (zmax0 zmin)=4, is calculated as 13 and 6, respectively, for the terrain profiles in Figs. 2(a) and 3(a).

In Fig. 2(b), the results for 435 MHz operating frequencyare presented over Hadsund terrain proﬁle, while the comparisons over Jer-

Fig. 3. Path loss over Jerslev terrain proﬁle. (a) Proﬁle geometry. (b) TM polarization at 970 MHz.Distance = 5600 m, 1 = 0 1 , =

185 066, = 124, = 6 .

slev proﬁle for 970 MHz are shown in Fig. 3(b). Both ﬁgures show the verygood agreement of the FBSA results with the measurements and the other IE method. Therefore, the FBSA can safelybe used as a reference solution to test the accuracyof the prediction of various ITU and FCC recommended propagation models.

B. Accuracy of the Prediction of ITU and FCC Propagation Models In Fig. 4, the accuracyof three empirical models are compared on an actual terrain proﬁle from Turkey. These models are ITU Recom- mendation Rec.-529 [2], [3], ITU Recommendation Rec.-1546 [4], and free space propagation model [5] with multiple diffraction. Note that, ITU Rec.-529 is the same as the Hata model [2] at 500 MHz. The MD correction used here is due to the Epstein–Peterson [7] in which obstruction from each knife-edge is added consecutively. The surface impedance is taken as a typical value ofs= 25 + j20 . The transmitter antenna is considered to be an isotropic radiator with a transmitted power of 50 W and a height of 20 m located at the left-most end of the terrain. The receiver antenna is taken as an isotropic radiator, too, having a height of 1.8 m. We have taken the strong region length,Ls, as 5 m for the terrain proﬁles in Figs. 4(a) and 5(a).

In Fig. 4(b), the results for the 200 MHz operating frequencyare presented for TM polarization. The free space propagation model with MD correction seems to have the best agreement with FBSA. The comparisons for 500 MHz are shown in Fig. 4(c) for TE polarization case. Nu- merical results show that the best agreement with FBSA results is obtained using free space propagation model with diffraction correction.

Also, ITU Rec.-529 results seem to reasonablyagree with the FBSA results especiallyat 500 MHz (Hata), while the poorest agreement is

(3)

3082 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005

Fig. 4. Total field over Cinarkoyterrain profile. (a) Profile geometry. (b) TM polarization at 200 MHz.Distance = 20 km, 1 = 0 1 ,

= 133 333, = 225, = 5 m. (c) TE polarization at 500 MHz.

Distance = 20 km, 1 = 0 1 , = 333 333, = 286,

= 5 m.

obtained for ITU Rec.-1546. We believe that, the use of ITU Rec.-1546 for propagation over rural areas will not be veryaccurate for ranges up to 20 km. In [4], it is stated that, the ITU Rec.-1546 should yield consistent results with Hata up to 20 km. However, the given Hata equation in the recommendation [4] is the one for urban areas and results in a difference around 25 dB in path loss from the rural Hata equation at 300 MHz [23]. Therefore, the ITU Rec.-1546 should be modiﬁed in order to be used for propagation over terrain proﬁles in rural areas.

The reason for the choice of the Epstein–Peterson method among the available MD corrections is explained with the aid of Fig. 5(b) and (c) for TM and TE polarizations, respectively. MD loss methods, Bullington [8], Vogler [10] and Epstein–Peterson [7], are examined in conjunction with free space propagation model in these ﬁgures. In Bullington method, all knife-edges are replaced byan equivalent one and in Vogler, Fresnel type integrals for each aperture is taken consecutively. Compar- isons show that the use of anyMD correction model yield quite similar results. However, a careful investigation of the ﬁgures show that, the Bullington method cannot catch the diffraction loss effects of some of the consecutive peaks that are close to each other. Vogler method is com- putationallyexpensive and yields quite similar results with Epstein–Pe- terson; still the least deviation from the reference solution occurs with the use of Epstein–Peterson. Therefore, the best choice for the multiple diffraction correction seems to be Epstein–Peterson.

The addition to MD losses to free space propagation, as in Figs. 4 and 5, predicts the ﬂuctuations in the ﬁeld strength due to terrain undulations.

the same idea can be applied to the empirical propagation models. The effect of using MD losses with empirical propagation models is shown explicitlyin Fig. 6. Free space propagation model, ITU Rec.-1546 and

Fig. 5. Comparisons of MDCs over Konya terrain proﬁle. (a) Proﬁle geometry. (b) TM polarization at 200 MHz. (c) TE polarization at 200 MHz.

Distance = 20 km, 1 = 0 1 , = 133 333, = 286,

= 5 m.

FCC curves, with and without MD corrections, are compared in terms of accuracyusing the FBSA as a reference, on the same geometrydepicted before in Fig. 4(a). The dotted lines in Fig. 6 represent the empirical models only, whereas the solid ones show the models with MD corrections. Reasonable agreement of free space and FCC results with the FBSA solution is observed in conjunction with (and without) MD corrections. In MD corrections, effects of the diffraction phenomenon is taken into account as an additional path loss only. Therefore, when used in conjunction with empirical curves, theyjust decrease the level of the curve along the portions of the terrain which are out of the lit region of the source. Hence, the use of MD losses together with empirical solutions mayincrease the error if the empirical curve is at a signiﬁcantly lower level than the reference solution. Thus, using MD losses with ITU Rec.-1546 increases the error. According to above observations, for the propagation over rural areas, ITU Rec.-1546 deviates much more than the older ITU recommended models.

IV. CONCLUSION

Most widelyused empirical propagation models with MD corrections for prediction of the field strengths over large terrain profiles have been investigated and observed that, theycannot provide a veryaccurate estimation of the scattered field or the path loss for an arbitraryenvironment, since theyare polarization independent and do not respond to changes in electrical properties of the terrain.

Furthermore, special care is needed when MD correction methods are used in conjunction with empirical solutions. Implementation of an MD correction method increases the error if the ﬁeld values due to an empirical model is alreadylower than the reference solution.

(4)

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 53, NO. 9, SEPTEMBER 2005 3083

Fig. 6. Comparisons of propagation models with and without MD corrections over Cinarkoyterrain proﬁle for TM polarization at 200 MHz.Distance =

20 km, 1 = 0 1 , = 133 333, = 225, = 5 m.

An interesting result of this studyis the accuracyof the Rec.-1546, which is one of the most recent ITU recommended propagation models.

For urban areas, it is consistent with Hata equations up to about 20 km, but for rural areas, predicted ﬁeld values of this model deviate from the reference solution more than those of the older ITU models do.

Therefore it needs to be modiﬁed for rural areas.

The results of this studymayhelp in the choice of the most preferable empirical models or in the development of more robust propagation techniques. A robust technique for the prediction of field strengths over large terrain profiles must be polarization and frequencydependent, and must take electrical properties, shadow and lit regions of the terrain profile into account.

ACKNOWLEDGMENT

The authors thank Prof. J. B. Andersen (Aalborg University, Den- mark) and his associates for kindlyproviding the terrain proﬁles and integral equation method results. Theyalso thank Dr. S. Topcu of Bilkent UniversityCommunications and Spectrum Management Research Center (ISYAM) for supplying implementations of empirical propagation models and multiple diffraction corrections.

REFERENCES

[1] Y. Okumura, E. Ohmori, T. Kawano, and K. Fukuda, “Field strength and its variabilityin vhf and uhf land-mobile radio service,” Rev. Elect.

Commun. Lab., vol. 16, pp. 825–873, Sep. 1968.

[2] M. Hata, “Empirical formula for propagation loss in land mobile radio services,” IEEE Trans. Veh. Technol., vol. 29, pp. 569–571, Aug. 1980.

[3] “Prediction Methods for the Terrestrial Land Mobile Service in the VHF and UHF Bands,” International Telecommunication Union , Recommen- dation ITU-R P.529–3, 1999.

[4] “Method for Point-to-Area Predictions for Terrestrial Services in the FrequencyRange 30 MHz to 3000 MHz,” International Telecommuni- cation Union, Recommendation ITU-R P.1546, 2001.

[5] “Calculation of Free-Space Attenuation,” International Telecommunica- tion Union, Recommendation ITU-R PN.525–2, 1994.

[6] “Propagation byDiffraction,” International Telecommunication Union, Recommendation ITU-R PN.526–7, 2001.

[7] J. Epstein and D. Peterson, “An experimental studyof wave propagation at 850 mhz,” Proc. IEEE, vol. 41, pp. 595–611, 1953.

[8] K. Bullington, “Radio propagation at frequencies above 30 megacycles,”

Proc. IRE, vol. 35, pp. 1122–1136, Oct. 1947.

[9] J. Deygout, “Multiple knife-edge diffraction of microwaves,” IEEE Trans. Antennas Propag., vol. AP-14, no. 4, pp. 480–489, Jul. 1966.

[10] L. E. Vogler, “An attenuation function for multiple knife-edge diffrac- tion,” Radio Sci., vol. 17, pp. 1541–1546, Nov. 1982.

[11] D. Holliday, L. L. D. Jr., and G. J. St.-Cyr, “Forward-backward: A new method for computing low-grazing scattering,” IEEE Trans. Antennas Propag., vol. 44, no. 5, pp. 722–729, May1996.

[12] H.-T. Chou and J. T. Johnson, “A novel acceleration for the computation of scattering from rough surfaces with the forward-backward method,”

Radio Sci., vol. 33, pp. 1277–1287, Jun. 1998.

[13] J. A. López, M. R. Pino, F. Obelleiro, and J. L. Rodríguez, “Applica- tion of the spectral acceleration forward-backward method to coverage analysis over terrain proﬁles,” J. Electromagn. Waves Appl., vol. 15, pp.

1049–1074, Aug. 2001.

[14] J. T. Hviid, J. B. Anderson, J. Toftgard, and J. Bojer, “Terrain based prop- agation model for rural area – An integral equations approach,” IEEE Trans. Antennas Propag., vol. 43, no. 1, pp. 41–46, Jan. 1995.

[15] R. Janaswamy, “A fredholm integral equation method for propagation over small terrain irregularities,” IEEE Trans. Antennas Propag., vol.

40, no. 9, pp. 1416–1422, Sep. 1994.

[16] J. T. Johnson, R. T. Shin, J. C. Eidson, L. Tsang, and J. A. Kong, “A method of moments model for vhf propagation,” IEEE Trans. Antennas Propag., vol. 45, no. 1, pp. 115–125, Jan. 1997.

[17] C. Brennan and P. J. Cullen, “Application of the fast far-ﬁeld approxi- mation to the computation of uhf pathloss over irregular terrain,” IEEE Trans. Antennas Propag., vol. 46, no. 6, pp. 881–890, Jun. 1998.

[18] , “Tabulated interaction method for uhf terrain propagation prob- lems,” IEEE Trans. Antennas Propag., vol. 46, no. 5, pp. 738–739, May 1998.

[19] C. L. Rino and H. D. Ngo, “Forward propagation in a half-space with an irregular boundary,” IEEE Trans. Antennas Propag., vol. 45, no. 9, pp.

1340–1347, Sep. 1997.

[20] C. L. Rino and V. R. Kruger, “A comparison of forward-boundary-in- tegral and parabolic-wave-equation propagation models,” IEEE Trans.

Antennas Propag., vol. 49, no. 4, pp. 574–582, Apr. 2001.

[21] F. K. Akorli and E. Costa, “An efﬁcient solution of an integral equation applicable to simulation of propagation along irregular terrain,” IEEE Trans. Antennas Propag., vol. 49, no. 7, pp. 1033–1036, Jul. 2001.

[22] T. B. A. Senior, “Impedance boundaryconditions for imperfectlycon- ducting surfaces,” Appl. Sci. Res., vol. 8, pp. 418–436, 1961.

[23] T. S. Rappaport, Wireless Communications: Principles and Practice, 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 2001.

A Low Proﬁle Single Dipole Antenna Radiating Circularly Polarized Waves

Fan Yang and Yahya Rahmat-Samii

Abstract—A low profile single dipole antenna that can generate circularly polarized (CP) radiation patterns is proposed in this paper. The CP patterns and low profile configuration are achieved using a speciallydesigned arti- ficial ground plane: a thin grounded slab loaded with periodic rectangular patches. The artificial ground plane exhibits in-phase reflection coefficients with polarization-dependent feature. The radiation mechanism of the an- tenna is described, and experimental results verifythe antenna concept.

Index Terms—Artiﬁcial ground plane, circular polarization, dipole an- tenna, low proﬁle.

Manuscript received January22, 2004; revised December 1, 2004.

F. Yang was with the Electrical Engineering Department, Universityof Cali- fornia, Los Angeles, CA 90095 USA. He is now with the Electrical Engineering Department, Universityof Mississippi, University, MS 38677 USA (e-mail:

fyang@olemiss.edu).

Y. Rahmat-Samii is with the Electrical Engineering Department, University of California, Los Angeles, CA 90095 (e-mail: rahmat@ee.ucla.edu).